## virtus Group Title Find the volume of the solid formed when the area bound by the curve y=4-x^2 and the x axis is rotated one complete revolution about the y axis 2 years ago 2 years ago

1. sauravshakya Group Title

first find the critical points and use integration

2. amistre64 Group Title

or just consider one side of it

3. virtus Group Title

can you just tell me the answer , because i am getting the wrong answer. I got 16 pi units but the answer is 8 pi units and i don't know where i went wrong.

4. virtus Group Title

*units ^3

5. amistre64 Group Title

6. amistre64 Group Title

|dw:1342094312271:dw| this can be done by shells or disks; which way are you most comfortable with?

7. amistre64 Group Title

i think i know why youre twice as big as the answer; your prolly integrating the whole thing across

8. amistre64 Group Title

your in effect sweeping the same volume twice when you do that

9. sauravshakya Group Title

10. amistre64 Group Title

|dw:1342094460320:dw| if we do shells:$\int_{0}^{2}2pix(4-x^2)dx$ $2pi\int_{0}^{2}x(4-x^2)dx$ $2pi\int_{0}^{2}4x-x^3\ dx$ $2pi\left(\frac{1}{2}4x^2-\frac{1}{4}x^4\right)_{0}^{2}$

11. virtus Group Title

oh i think i understand. I apologise amistre64 if i sounded rude before. I had no intentions whatsoever to offend you.

12. amistre64 Group Title

no offense taken :)

13. virtus Group Title

@amistre64 i thought it was around y axis, shouldn't be dy not dx ?

14. amistre64 Group Title

depends on your method; i used the shell method, which opens up along the x axis the disc method would travel along the y

15. amistre64 Group Title

teh disc method we would have to convert y=x into its inverse x=y, which isnt that hard to do, but just takes extra steps :)

16. virtus Group Title

oh i see, so for the shell method where does the x come from in x(4-x^2)

17. amistre64 Group Title

think of the shell method as finding the area of a sheet of paper, or a flattened out tin can. the width of the paper is the circumference of the base circle|dw:1342095061762:dw| the height of the paper is the function that it hits along the way. Area = base (2pi x) * height (f(x))

18. amistre64 Group Title

|dw:1342095194082:dw|

19. virtus Group Title

OH I GET IT NOW ! thanks @amistre64

20. amistre64 Group Title

youre welcome